List of top Questions asked in JEE Main- 2020

The correct match between the entries in column I and column II are :

I	II
Radiation	Wavelength
(a) Microwave	(i) 100 m
(b) Gamma rays	(ii) \(10^{-15}\) m
(c) A.M. radio waves	(iii) \(10^{-10}\) m
(d) X-rays	(iv) \(10^{-3}\) m

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is :

In the circuit shown, charge on the \(5\ \mu\mathrm{F}\) capacitor is :

A parallel plate capacitor has plate of length 'l', width 'w' and separation of plates is 'd'. It is connected to a battery of emf V. A dielectric slab of the same thickness 'd' and of dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period \(T_1\) and,
(ii) back and forth in a direction perpendicular to its plane, with a period \(T_2\). The ratio \(\frac{T_1}{T_2}\) will be :

Two Zener diodes (A and B) having breakdown voltages of 6 V and 4 V respectively, are connected as shown in the circuit below. The output voltage \(V_0\) variation with input voltage linearly increasing with time, is given by :
(\(V_{input}\) = 0 V at t = 0)
(figures are qualitative)

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate \(\frac{dM(t)}{dt} = bv^2(t)\), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

Two coherent sources of sound, \(S_1\) and \(S_2\), produce sound waves of the same wavelength, \(\lambda\) = 1 m, in phase. \(S_1\) and \(S_2\) are placed 1.5 m apart (see fig). A listener, located at L, directly in front of \(S_2\) finds that the intensity is at a minimum when he is 2 m away from \(S_2\). The listener moves away from \(S_1\), keeping his distance from \(S_2\) fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from \(S_1\). Then, d is :

The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is \(\omega\). An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is (h << R, where R is the radius of the earth)

If the lines \(x + y = a\) and \(x - y = b\) touch the curve \(y = x^2 - 3x + 2\) at the points where the curve intersects the x-axis, then \(\dfrac{a}{b}\) is equal to _______.

The coefficient of \(x^4\) in the expansion of \((1 + x + x^2 + x^3)^6\) in powers of \(x\), is ______.

In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is __________.

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is :

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2^o, its figure of merit is close to :

Two different wires having lengths \(L_1\) and \(L_2\), and respective temperature coefficient of linear expansion \(\alpha_1\) and \(\alpha_2\), are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

If the line \(y = mx + c\) is a common tangent to the hyperbola
\(\dfrac{x^2}{100} - \dfrac{y^2}{64} = 1\)
and the circle \(x^2 + y^2 = 36\), then which one of the following is true?

If for some \(\alpha \in \mathbb{R}\), the lines
\(L_1 : \dfrac{x+1}{2} = \dfrac{y-2}{-1} = \dfrac{z-1}{1}\)
and
\(L_2 : \dfrac{x+2}{\alpha} = \dfrac{y+1}{5-\alpha} = \dfrac{z+1}{1}\)
are coplanar, then the line \(L_2\) passes through the point :

Let the vectors \(\vec{a}, \vec{b}, \vec{c}\) be such that \(|\vec{a}| = 2\), \(|\vec{b}| = 4\) and \(|\vec{c}| = 4\). If the projection of \(\vec{b}\) on \(\vec{a}\) is equal to the projection of \(\vec{c}\) on \(\vec{a}\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), then the value of \(|\vec{a} + \vec{b} - \vec{c}|\) is ___________.

Which of the following points lies on the tangent to the curve
\(x^4 e^y + 2\sqrt{y+1} = 3\) at the point \((1, 0)\)?

Let \(A = \{a, b, c\}\) and \(B = \{1, 2, 3, 4\}\). Then the number of elements in the set \(C = \{f : A \to B \mid 2 \in f(A)\text{ and } f\text{ is not one-one}\}\) is ______.

If the sum of the first 20 terms of the series
\(\log_{(7^{1/2})}x + \log_{(7^{1/3})}x + \log_{(7^{1/4})}x + \ldots\)
is \(460\), then \(x\) is equal to :

The statement
\((p \to (q \to p)) \to (p \to (p \vee q))\) is :

The derivative of
\(\tan^{-1}\left(\dfrac{\sqrt{1+x^2} - 1}{x}\right)\)
with respect to
\(\tan^{-1}\left(\dfrac{2x\sqrt{1-x^2}}{1-2x^2}\right)\)
at \(x = \dfrac{1}{2}\) is :

Let \(y=y(x)\) be the solution of the differential equation \( \cos x\,\frac{dy}{dx}+2y\sin x=\sin2x,\ x\in\left(0,\frac{\pi}{2}\right) \). If \( y\left(\frac{\pi}{3}\right)=0 \), then \( y\left(\frac{\pi}{4}\right) \) is equal to :

If \(a + x = b + y = c + z + 1\), where \(a, b, c, x, y, z\) are non-zero distinct real numbers, then
\(\begin{vmatrix} x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c \end{vmatrix}\)
is equal to :